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A234007
Free polyominoes with 4n squares, having 90-degree rotational symmetry about a square corner, but not having reflective symmetry.
12
0, 1, 2, 9, 30, 110, 387, 1419, 5185, 19225, 71634, 269250, 1017260, 3864267, 14742260, 56470053, 217052829, 836878982
OFFSET
1,3
COMMENTS
The number of free polyominoes of size 4n that have 90-degree rotational symmetry about a point that coincides with the corner of a square, and that have not at the same time reflective symmetry. Note that for polyominoes which have a hole in the center, the center of rotation will be the corner of a square within the hole, rather than being the corner of a square of the polyomino itself. The sequence is defined for 4n rather than n as polyominoes of size not a multiple of 4 cannot have the required symmetry.
The sequence enumerates a subset of the polyominoes enumerated by A144553.
KEYWORD
nonn,more
AUTHOR
John Mason, Dec 18 2013
EXTENSIONS
a(8)-a(13) from Sean A. Irvine, Jul 04 2019
a(14)-a(18) from John Mason, Feb 02 2022
STATUS
approved